Based on the type of equations in the system, what is the greatest possible number of solutions (x2+y2=9/9x+2y=16?
2 answers:
Answer:
`Option B.
Step-by-step explanation:
The given system of equations is
The graph of first equation is circle and the graph of second equation is a line.
We know that a line can intersect a circle at most 2 times. So, the greatest possible number of solutions is 2.
First equation can be rewritten as
It is the standard form of a circle , where (h,k) is center and r is radius.
In the above equation h=0,k=0 and r=3. It is a circle with radius 3 and centered at origin.
The second equation is
It is a linear equation.
Table of values.
x y
0 8
1 3.5
2 -1
Plot these points on a coordinate plane and connect them by a straight line.
From the below graph it is clear that the line and circle intersect each other at two points. So, the given system of equation have two solutions.
Therefore, the correct option is B.
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